MARSSparamCIs: Standard Errors, Confidence Intervals and Bias for MARSS...

In MARSS: Multivariate Autoregressive State-Space Modeling

Standard Errors, Confidence Intervals and Bias for MARSS Parameters

Description

Computes standard errors, confidence intervals and bias for the maximum-likelihood estimates of MARSS model parameters. If you want confidence intervals on the estimated hidden states, see print.marssMLE() and look for states.cis.

Usage

MARSSparamCIs(MLEobj, method = "hessian", alpha = 0.05, nboot =
    1000, silent = TRUE, hessian.fun = "Harvey1989")

Arguments

MLEobj	An object of class marssMLE. Must have a $par element containing the MLE parameter estimates.
method	Method for calculating the standard errors: "hessian", "parametric", and "innovations" implemented currently.
alpha	alpha level for the 1-alpha confidence intervals.
nboot	Number of bootstraps to use for "parametric" and "innovations" methods.
hessian.fun	The function to use for computing the Hessian. Options are "Harvey1989" (default analytical) or two numerical options: "fdHess" and "optim". See MARSShessian.
silent	If false, a progress bar is shown for "parametric" and "innovations" methods.

Details

Approximate confidence intervals (CIs) on the model parameters may be calculated from the observed Fisher Information matrix ("Hessian CIs", see MARSSFisherI()) or parametric or non-parametric (innovations) bootstrapping using nboot bootstraps. The Hessian CIs are based on the asymptotic normality of MLE parameters under a large-sample approximation. The Hessian computation for variance-covariance matrices is a symmetric approximation and the lower CIs for variances might be negative. Bootstrap estimates of parameter bias are reported if method "parametric" or "innovations" is specified.

Note, these are added to the par elements of a marssMLE object but are in "marss" form not "marxss" form. Thus the MLEobj$par.upCI and related elements that are added to the marssMLE object may not look familiar to the user. Instead the user should extract these elements using print(MLEobj) and passing in the argument what set to "par.se","par.bias","par.lowCIs", or "par.upCIs". See print(). Or use tidy().

Value

MARSSparamCIs returns the marssMLE object passed in, with additional components par.se, par.upCI, par.lowCI, par.CI.alpha, par.CI.method, par.CI.nboot and par.bias (if method is "parametric" or "innovations").

Author(s)

Eli Holmes, NOAA, Seattle, USA.

References

Holmes, E. E., E. J. Ward, and M. D. Scheuerell (2012) Analysis of multivariate time-series using the MARSS package. NOAA Fisheries, Northwest Fisheries Science Center, 2725 Montlake Blvd E., Seattle, WA 98112 Type RShowDoc("UserGuide",package="MARSS") to open a copy.

See Also

MARSSboot(), MARSSinnovationsboot(), MARSShessian()

Examples

dat <- t(harborSealWA)
dat <- dat[2:4, ]
kem <- MARSS(dat, model = list(
  Z = matrix(1, 3, 1),
  R = "diagonal and unequal"
))
kem.with.CIs.from.hessian <- MARSSparamCIs(kem)
kem.with.CIs.from.hessian

MARSS documentation built on May 29, 2024, 3:34 a.m.